Dynamic Computer Algebra System
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Dcas is a dynamic computer algebra system featuring the idea of using identities as rules for manipulation of algebra. Robert Fenichel developed a system called FAMOUS in the 1970s using the LISP programming language pursuing the same aim.
A modern system DCAS has been implemented by Martin Johansen called DCAS Ether. The system works by selecting a class of identities based on the form of the input expression. DCAS Ether is licensed under the GNU GPL.
Here are two examples of identity collections, one for basic algebra, the other for Boolean algebra.
/* Distributivity */
x*(a + b) = a*x + b*x;
/* Powers */
(a*b)^c = a^c*b^c;
(a^b)^c = a^(b*c);
/* add, sub */
solveequ(x, (gfvi(f(x)) + gfve(a(x)) = gfve(b(x)))) = solveequ(x, f = b - a);
solveequ(x, (gfvi(f(x)) + gfve(a(x)) + c = gfve(b(x)))) = solveequ(x, f + c = b - a);
/* mul, div */
solveequ(x, (gfvi(f(x))*gfve(a(x))*c = gfve(b(x)))) = solveequ(x, f*c = b/a);
solveequ(x, gfvi(f(x))*gfve(a(x)) = gfve(b(x))) = solveequ(x, f = b/a);
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